Thermal Conductivity in the Vicinity of the Quantum Critical End Point in ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$

Thermal conductivity of ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ was measured down to 40 mK and at magnetic fields through the quantum critical end point at $H_c=7.85\mathrm{T}$. A peak in the electrical resistivity as a function of the field was mimicked by the thermal resistivity. In the limit as $T\to 0\mathrm{K}$, we find that the Wiedemann-Franz law is satisfied to within 5% at all fields, implying that there is no breakdown of the electron despite the destruction of the Fermi liquid state at quantum criticality. A significant change in disorder [from ${\rho }_0(H=0\mathrm{T})=2.1$ to $0.5\mu \Omega \mathrm{cm}$] does not influence our conclusions. At finite temperatures, the temperature dependence of the Lorenz number is consistent with ferromagnetic fluctuations causing the non-Fermi liquid behavior as one would expect at a metamagnetic quantum critical end point.

Figure 1

High temperature thermal conductivity at several fields along the $c$ axis including the critical field. The heat current was applied in the $ab$ plane. The dashed line is an estimate of the phonon conductivity obtained by considering the WFL as discussed later in the text.

Figure 2

A comparison of heat ($\kappa /T$) and charge ($L_0/\rho$) conductivities at several fields versus $T$ at low temperature. These quantities extrapolate to the same value at $T=0$ if the Wiedemann-Franz law is to be satisfied. Solid lines are fits to $\rho ={\rho }_0+A{T}^2$. The dashed line for $H_c$ is a linear fit below 0.8 K. (b) Comparing two samples with different amounts of disorder. Sample 2 has been rotated by 20° with respect to the $c$ axis, which mainly changes the value of the critical field.

Figure 3

Verification of the Wiedemann-Franz law from field sweeps of the Lorenz number. Inset: Field sweeps of heat ($\kappa /T$) and charge ($L_0/\rho$) conductivity at low temperature.

Figure 4

(a) Temperature dependence of the electronic contribution to the Lorenz ratio $L(T)$, which is consistent with the standard picture for itinerant electron metamagnetism. (b) The thermal resistance $W_{\mathrm{SF}}\equiv 1/{\kappa }_{\mathrm{el}}-{\rho }_0/L_{0}T$ attributed to scattering off of spin fluctuations.